What is the derivate of...?

Question

#sin(xy)+e^(xy)=e^x#

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Answer 1 · 2018-06-12T00:05:41

#y'= (e^x-y(cosx(xy)+e^(xy)))/(x(cosx(xy)+e^(xy)))#

Differentiate both sides of the equation:

#d/dx (sin(xy)+e^(xy)) = d/dx e^x#

#(y+xy')cosx(xy)+(y+xy')e^(xy) = e^x#

#y(cosx(xy)+e^(xy)) +xy'(cosx(xy)+e^(xy)) = e^x#

Solve now for #y'#:

#y'= (e^x-y(cosx(xy)+e^(xy)))/(x(cosx(xy)+e^(xy)))#